Given: Points P,Q,R, and S are collinear

Question

Prove: PQ=PS-WS

Answer 1

To prove that PQ = PS - WS, we need to use the fact that points P, Q, R, and S are collinear.

Let's draw a line segment PR and extend it to point S. So, we have a line segment PQ and a line segment PS, with point R in between them.

Since points P, Q, R, and S are collinear, the distance between P and R plus the distance between R and S should be equal to the distance between P and S.

So, we can say that PR + RS = PS.

Now, we can subtract WS from both sides of the equation:

PR + RS - WS = PS - WS.

Since PQ is equal to PR, we can substitute PR with PQ in the equation:

PQ + RS - WS = PS - WS.

Finally, we can simplify the equation:

PQ + RS - WS = PS - WS.

By subtracting WS from both sides, we have:

PQ + RS = PS.

Therefore, we have proven that PQ = PS - WS using the fact that points P, Q, R, and S are collinear.